Details

analyze2.5s

Algorithm: search

sample500.0ms

Algorithm

intervals

Results

169.0ms	20×	body	5120	invalid
92.0ms	114×	body	1280	valid
80.0ms	35×	body	2560	invalid
46.0ms	30×	body	2560	valid
37.0ms	63×	body	640	valid
19.0ms	23×	body	1280	invalid
13.0ms	5×	body	5120	valid
9.0ms	18×	body	640	invalid
5.0ms	14×	body	320	valid
4.0ms	28×	body	80	invalid
3.0ms	20×	body	80	valid
3.0ms	10×	body	160	valid
2.0ms	7×	body	320	invalid
1.0ms	5×	body	160	invalid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (25.0ms)

Iter	Nodes	Cost
0	44	13
1	147	13
2	857	12
3	5002	11

prune14.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 40.6b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
0.6b	(* (pow t 3.0) (tan k))
19.8b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
30.2b	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

392×	`add-exp-log`
265×	`prod-exp`
74×	`div-exp` `add-cbrt-cube`
61×	`pow-exp`
41×	`pow-to-exp`
40×	`cbrt-unprod`
25×	`associate-l`
21×	`add-sqr-sqrt`
17×	`unpow-prod-down`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-undiv`
10×	`times-frac`
7×	`associate-r/` `associate-r*`
6×	`pow1`
4×	`tan-quot` `add-log-exp`
3×	`*-commutative` `unswap-sqr` `sqr-pow`
2×	`associate-*l/` `div-inv`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `associate-/r/` `associate-/l`

Counts

4 → 185

Calls

4 calls:

15.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
5.0ms	(* (pow t 3.0) (tan k))
17.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
11.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

series304.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k))
52.0ms	(* (pow t 3.0) (tan k))
113.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k))) (sin k)))
67.0ms	(* (pow (/ k t) 2.0) (* (pow t 3.0) (tan k)))

simplify43.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1064	2314
1	5002	1928

prune293.0ms

Filtered

84 candidates to 197 candidates (-134.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	185	12	197
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	187	12	199

Merged error: 26.1b

Counts

199 → 12

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (pow t 3.0) (tan k))
15.4b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
19.6b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
19.8b	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

1610×	`add-exp-log`
1168×	`prod-exp`
346×	`div-exp`
341×	`pow-exp`
205×	`pow-to-exp`
95×	`add-cbrt-cube`
55×	`cbrt-unprod`
41×	`associate-l`
30×	`unpow-prod-down`
28×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`cbrt-undiv`
9×	`associate-*r/`
5×	`associate-r`
4×	`tan-quot` `pow1` `add-log-exp` `sqr-pow`
3×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-l/` `clear-num` `associate-/r` `associate-/r/` `associate-/l*`

Counts

4 → 408

Calls

4 calls:

5.0ms	(* (pow t 3.0) (tan k))
16.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
11.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
28.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (pow t 3.0) (tan k))
68.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
67.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))
113.0ms	(/ (* 2.0 (* l l)) (* (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (sin k)))

simplify83.0ms

Algorithm

egg-herbie

Counts

420 → 420

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1771	6487
1	5001	5612

prune425.0ms

Filtered

111 candidates to 420 candidates (-278.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	416	4	420
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	419	13	432

Merged error: 26.1b

Counts

432 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

2.7b	(/ (* l l) (sin k))
15.4b	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
18.7b	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
19.6b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

1610×	`add-exp-log`
1029×	`prod-exp`
485×	`div-exp`
340×	`pow-exp`
204×	`pow-to-exp`
98×	`add-cbrt-cube`
48×	`cbrt-unprod`
42×	`associate-l`
30×	`add-sqr-sqrt`
28×	`times-frac`
26×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
24×	`cbrt-undiv`
9×	`associate-r/` `associate-r*`
6×	`pow1`
5×	`div-inv`
4×	`add-log-exp`
3×	`tan-quot` `associate-/r` `-commutative`
2×	`unswap-sqr` `sqr-pow`
1×	`frac-times` `frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `associate-/r/` `associate-/l`

Counts

4 → 418

Calls

4 calls:

4.0ms	(/ (* l l) (sin k))
16.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
28.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
12.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* l l) (sin k))
68.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))
196.0ms	(* (/ 2.0 (* (pow (/ k t) (/ 2.0 2)) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k))))) (/ (* l l) (sin k)))
71.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify87.0ms

Algorithm

egg-herbie

Counts

430 → 430

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1730	6648
1	5001	5458

prune383.0ms

Filtered

108 candidates to 430 candidates (-298.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	424	6	430
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	427	16	443

Merged error: 22.2b

Counts

443 → 16

localize24.0ms

Local error

Found 4 expressions with local error:

2.7b	(/ (* l l) (sin k))
13.7b	(* (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
16.9b	(* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
19.6b	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

2259×	`add-exp-log`
1240×	`prod-exp`
875×	`div-exp`
338×	`pow-exp`
217×	`add-cbrt-cube`
207×	`pow-to-exp`
178×	`times-frac`
134×	`associate-l`
106×	`add-sqr-sqrt`
105×	`cbrt-unprod`
102×	`add-cube-cbrt` `*-un-lft-identity`
91×	`unpow-prod-down`
66×	`cbrt-undiv`
54×	`sqrt-prod`
11×	`pow1` `div-inv`
10×	`associate-*r/`
9×	`associate-r`
7×	`sqr-pow`
6×	`frac-times`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
3×	`associate-/r` `-commutative`
2×	`tan-quot` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r/` `associate-/l*`

Counts

4 → 589

Calls

4 calls:

5.0ms	(/ (* l l) (sin k))
40.0ms	(* (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
19.0ms	(* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
12.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ (* l l) (sin k))
200.0ms	(* (/ (sqrt 2.0) (pow (/ k t) (/ 2.0 2))) (* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k))))
191.0ms	(* (/ (sqrt 2.0) (* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))) (/ (* l l) (sin k)))
68.0ms	(* (pow (/ k t) (/ 2.0 2)) (* (pow t 3.0) (tan k)))

simplify139.0ms

Algorithm

egg-herbie

Counts

601 → 601

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	2394	11773
1	5001	10742

prune899.0ms

Filtered

194 candidates to 601 candidates (-209.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	595	6	601
Fresh	3	11	14
Picked	1	0	1
Done	1	0	1
Total	600	17	617

Merged error: 20.5b

Counts

617 → 17

regimes758.0ms

Accuracy

41.1% (6.8b remaining)

Error of 27.8b against oracle of 20.9b and baseline of 32.6b

bsearch4.0s

Steps

Iters	Range	Point
10	5.801551871162295e-125	3.3824113800593744e-113	3.332827288397092e-113
9	-2.0779099954646202e-299	-7.092354111441479e-308	-7.214671103543182e-308
10	-8.71438938555453e-104	-1.1510719557072309e-119	-2.1282463353639212e-108

Iters

Range

Point

5.801551871162295e-125

3.3824113800593744e-113

3.332827288397092e-113

-2.0779099954646202e-299

-7.092354111441479e-308

-7.214671103543182e-308

-8.71438938555453e-104

-1.1510719557072309e-119

-2.1282463353639212e-108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	97	91
1	97	91

end0.0ms

analyze2.7s

Algorithm: search

sample14.9s

Algorithm

intervals

Results

3.7s	757×	body	5120	invalid
3.2s	1289×	body	2560	invalid
2.8s	3370×	body	1280	valid
1.3s	930×	body	2560	valid
1.1s	1962×	body	640	valid
687.0ms	210×	body	5120	valid
665.0ms	800×	body	1280	invalid
288.0ms	561×	body	640	invalid
259.0ms	633×	body	320	valid
130.0ms	933×	body	80	invalid
128.0ms	340×	body	320	invalid
94.0ms	653×	body	80	valid
68.0ms	242×	body	160	valid
56.0ms	211×	body	160	invalid

Details

analyze2.5s

sample500.0ms

simplify27.0ms

prune14.0ms

localize20.0ms

rewrite60.0ms

series304.0ms

simplify43.0ms

prune293.0ms

localize24.0ms

rewrite109.0ms

series300.0ms

simplify83.0ms

prune425.0ms

localize21.0ms

rewrite109.0ms

series345.0ms

simplify87.0ms

prune383.0ms

localize24.0ms

rewrite155.0ms

series470.0ms

simplify139.0ms

prune899.0ms

regimes758.0ms

bsearch4.0s

simplify2.0ms

end0.0ms

analyze2.7s

sample14.9s

Profiling